Series vs parallel resistor combinations — Hinglish notes

1.2.1 · Hardware › Circuit Analysis Fundamentals

Hum resistors ko combine karte hi kyun hain?

Real circuits mein kaafi saare resistors hote hain. Current aur voltage predict karne ke liye hum ek cluster of resistors ko ek equivalent resistor $R_{e q}$ se replace karna chahte hain jo do terminals ke nazariye se bilkul same behave kare. "Same behave kare" ka matlab hai: un do terminals par same voltage lagao, to same total current bahega.

Neeche sab kuch sirf do laws se derive hua hai:

SERIES — $R_{e q} = R_{1} + R_{2} + \dots$ derive karna

WHAT hai series? Resistors series mein hote hain agar unse same current guzre — yeh ek single path par end-to-end rakhe hote hain, beech mein koi branch nahi hoti.

HOW derive karein: $R_{1}, R_{2}$ ko line mein rakho, dono se current $I$ bahao (same $I$ — yahi definition hai). KVL se total voltage, drops ka sum hoga:

$V = V_{1} + V_{2} = I R_{1} + I R_{2} = I (R_{1} + R_{2})$

Lekin equivalent resistor ko $V = I R_{e q}$ satisfy karna chahiye. Match karne par:

PARALLEL — $\frac{1}{R _{e q}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots$ derive karna

WHAT hai parallel? Resistors parallel mein hote hain agar unke across same voltage ho — dono same do nodes ke beech connected hon.

HOW derive karein: Dono ke across voltage $V$ lagao. Har ek apna khud ka current carry karta hai (Ohm):

$I_{1} = \frac{V}{R _{1}}, I_{2} = \frac{V}{R _{2}}$

KCL se total current sum hoga:

$I = I_{1} + I_{2} = \frac{V}{R _{1}} + \frac{V}{R _{2}} = V (\frac{1}{R _{1}} + \frac{1}{R _{2}})$

Equivalent ko $I = V / R_{e q}$ dena chahiye, to $V$ se divide karne par:

Kyun chhhota? Ek parallel path add karne se current ko bahne ka ek aur rasta mil jaata hai — tum isse kabhi mushkil nahi banaate, sirf aasaan karte ho, isliye resistance sirf neeche hi ja sakti hai.

Figure — Series vs parallel resistor combinations

Worked examples

Forecast-then-Verify

Recall Compute karne se pehle forecast karo

Q: Tumhare paas $6 Ω$ aur $3 Ω$ hain. Kaun sa arrangement $2 Ω$ dega? Kaun sa $9 Ω$ dega? Verify: Parallel: $\frac{6 \cdot 3}{9} = 2 Ω$ . Series: $6 + 3 = 9 Ω$ . Parallel < smallest (3), series > largest (6). ✓

Common mistakes (Steel-manned)

Feynman

Recall Ek 12-saal ke bachche ko explain karo

Socho water pipes. Series ek lambi pipe hai jo narrow sections ko end-to-end jodkar bani hai — poori cheez mein paani dhakkelna kisi bhi ek section se mushkil hai, isliye "resistances" pile up hoti hain. Parallel aise hai jaise same do tanks ke beech extra pipes side by side drill karo — ab paani ke paas bahne ke liye zyada openings hain, to yeh aasaan hai, aur combined "resistance" akele ki aasaan single pipe se bhi chhhoti hoti hai. Isliye: series adds, parallel drops below the smallest.

Flashcards

Series mein, sabhi resistors mein kya shared hota hai?

Same current (voltages KVL se add hoti hain).

Parallel mein, sabhi resistors mein kya shared hota hai?

Same voltage (currents KCL se add hote hain).

Series equivalent resistance formula?

R_{e q} = R_{1} + R_{2} + \dots

Parallel equivalent resistance formula?

\frac{1}{R _{e q}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots

Do-resistor parallel shortcut?

R_{e q} = \frac{R _{1} R _{2}}{R _{1} + R _{2}}

(product over sum).

Kya series

R_{e q}

har resistor se bada hai ya chhhota?

Bada (hamesha ≥ largest).

Kya parallel

R_{e q}

har resistor se bada hai ya chhhota?

Chhhota (hamesha < smallest).

n

equal resistors

R

parallel mein kya dete hain?

R / n

Parallel mein resistor add karne par resistance kyun girta hai?

Yeh current ko ek aur rasta deta hai, jo flow ko sirf aasaan hi bana sakta hai.

Kaun sa law series voltages ko add karta hai?

Kirchhoff's Voltage Law (KVL).

Kaun sa law parallel currents ko add karta hai?

Kirchhoff's Current Law (KCL).

Series divider mein, kaun sa resistor zyada voltage drop karta hai?

Bada wala (

V_{i} = I R_{i}

Connections

Ohms Law — $V = I R$ foundation jo har derivation use karta hai.
Kirchhoffs Voltage Law & Kirchhoffs Current Law — jahan se "voltages add / currents add" aata hai.
Voltage Divider & Current Divider — series/parallel ke direct consequences.
Equivalent Resistance and Network Reduction — ladders ko step by step collapse karna.
Conductance — parallel conductances ke liye "series" jaisa hai.
Power Dissipation in Resistors — $P = I^{2} R$ har resistor ke liye, currents find karne ke baad.